Lounging and going barefoot are not safety issues, unless you consider all forms of unconventionality to be unprofessional, and all forms of unprofessionalism to be irresponsible.

It’s a morale issue, which a competent captain would be aware of. Crew members see that and think “if the captain doesn’t give a shit, why should I?” Crew starts blowing off their duties which would ultimately result in a safety issue.

There’s a reason why people in positions of responsibility behave the way they do when in front of others. I’m sure Picard lounged around in his quarters reading books or whatever, but when called to the bridge he’d put on his game face and behave in a way that commands respect in front of the crew. It’s part of the job of being captain.